Heat grill to medium-low or grill pan over medium heat.
Brush cut sides of peaches with oil.
Place peach halves on grill, cut sides down and grill for 3-4 minutes until gently charred.
Turn peaches over and grill other side until peaches are soft and warmed through.
Remove peaches from grill to a plate and allow to rest.
While peaches are grilling, make honey walnuts:
Heat butter in sauté pan over low heat until bubbling.
Add honey, salt and stir until combined. Add walnuts and stir to coat.
Cook until walnuts are toasted and honey and butter are almost completely absorbed.
Transfer walnuts from pan to parchment paper, spread walnuts out and allow to cool.
When ready to serve: Place a scoop of ice cream in a small bowl or dish with high sides.
Spoon two grilled peach wedges around each scoop of ice cream.
Top each serving with ¼ of prepared honey walnuts.